(2k+1)(k+4)=0

Solution for (2k+1)(k+4)=0 equation:

Simplifying
(2k + 1)(k + 4) = 0

Reorder the terms:
(1 + 2k)(k + 4) = 0

Reorder the terms:
(1 + 2k)(4 + k) = 0

Multiply (1 + 2k) * (4 + k)
(1(4 + k) + 2k * (4 + k)) = 0
((4 * 1 + k * 1) + 2k * (4 + k)) = 0
((4 + 1k) + 2k * (4 + k)) = 0
(4 + 1k + (4 * 2k + k * 2k)) = 0
(4 + 1k + (8k + 2k2)) = 0

Combine like terms: 1k + 8k = 9k
(4 + 9k + 2k2) = 0

Solving
4 + 9k + 2k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4 + k)(1 + 2k) = 0

Subproblem 1
Set the factor '(4 + k)' equal to zero and attempt to solve:

Simplifying
4 + k = 0

Solving
4 + k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + k = 0 + -4
k = 0 + -4

Combine like terms: 0 + -4 = -4
k = -4

Simplifying
k = -4
Subproblem 2
Set the factor '(1 + 2k)' equal to zero and attempt to solve:

Simplifying
1 + 2k = 0

Solving
1 + 2k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2k = 0 + -1
2k = 0 + -1

Combine like terms: 0 + -1 = -1
2k = -1

Divide each side by '2'.
k = -0.5

Simplifying
k = -0.5
Solution
k = {-4, -0.5}